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Adaptive Iterated Local Search with Random Restarts for the Balanced Travelling Salesman Problem

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Book cover Metaheuristics for Combinatorial Optimization (MESS 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1332))

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Abstract

Metaheuristics have been widely used to solve NP-hard problems, with excellent results. Among all NP-hard problems, the Travelling Salesman Problem (TSP) is potentially the most studied one. In this work, a variation of the TSP is considered; the main differences being, edges may have positive or negative costs and the objective is to return a Hamiltonian cycle with cost as close as possible to zero. This variation is called the balanced TSP (BTSP). To tackle this new problem, we present an adaptive variant of the iterated local search metaheuristic featuring also random restart. This algorithm was tested on the MESS2018 metaheuristic competition and achieved notable results, scoring the 5th position overall. In this paper, we detail all the components of the algorithm itself and present the best solutions identified. Even though this metaheuristic was tailored for the BTSP, with small modifications its structure can be applied to virtually any NP-hard problem. In particular, we introduce the uneven reward-and-punishment rule which is a powerful tool, applicable in many contexts where fast responses to dynamic changes are crucial.

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Notes

  1. 1.

    !! is double factorial, i.e. \(f!!= f \cdot (f-2)\cdot (f-4)..\).

    In our case, \(10!!=3840\).

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Acknowledgement

The authors want to thank the organisers of the MESS2018 summer school for the challenging opportunity they offered us. The first author wants to acknowledge the DIAMANT mathematics cluster for partially funding his work.

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Jacopo Pierotti & J. Theresia van Essen

  2. Faculty of Informatics, Università della Svizzera italiana, Lugano, Switzerland

    Lorenzo Ferretti & Laura Pozzi

Authors
  1. Jacopo Pierotti
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  2. Lorenzo Ferretti
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  3. Laura Pozzi
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  4. J. Theresia van Essen
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Corresponding author

Correspondence to Jacopo Pierotti .

Editor information

Editors and Affiliations

  1. Department of Economics and Business, University of Catania, Catania, Italy

    Salvatore Greco

  2. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    Mario F. Pavone

  3. Laboratoire Cristal, University of Lille and Inria, Lille, France

    El-Ghazali Talbi

  4. Department of Electrical, Electronics, and Information Engineering and CIRI-ICT, University of Bologna, Bologna, Italy

    Daniele Vigo

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Pierotti, J., Ferretti, L., Pozzi, L., van Essen, J.T. (2021). Adaptive Iterated Local Search with Random Restarts for the Balanced Travelling Salesman Problem. In: Greco, S., Pavone, M.F., Talbi, EG., Vigo, D. (eds) Metaheuristics for Combinatorial Optimization. MESS 2018. Advances in Intelligent Systems and Computing, vol 1332. Springer, Cham. https://doi.org/10.1007/978-3-030-68520-1_4

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